Which of the following relation is/are true? & I. ( 27 )^1/3 ( 13 )…

Question

Which of the following relation is/are true? & I. ( 27 )^1/3 > ( 13 )^1/2 < ( 47 )^1/6 & II. ( 23 )^1/3 < ( 49 )^1/2 < ( 52 )^1/6 & III. ( 53 )^1/6 < ( 41 )^1/3 < ( 37 )^1/2

Accepted Answer

Option A. Only III. Answer & Solution Answer: Option A Solution: & Take LCM of ( 2,\,3\,\& \,6 ) = 6 & I. ( 27 )^1/3 > ( 13 )^1/2 ( 13 )^ 32 × 3 ( 13 )^3/6 ( 2197 )^1/6 < ( 47 )^1/6 & This statement is false & II. ( 23 )^1/3 < ( 49 )^1/2 < ( 52 )^1/6 & = ( 23 )^ 23 × 2 < ( 49 )^ 32 × 3 < ( 52 )^ 1…